Simplifying Radical Expressions: Intro to Conjugates
Read this topicProblems 27
- Simplify. 3x−4x+5\frac{3x-4}{x+\sqrt{5}}x+53x−4
- Simplify. 4−413+11\frac{4-\sqrt{4}}{\sqrt{13}+\sqrt{11}}13+114−4
- Simplify. 1(5+6)2\frac{1}{(\sqrt{5}+\sqrt{6})^2}(5+6)21
- Simplify. 51+2\frac{5}{1+\sqrt{2}}1+25
- Simplify. 67−5\frac{6}{7-\sqrt{5}}7−56
- Simplify. 46−8\frac{4}{\sqrt{6}-\sqrt{8}}6−84
- Simplify. 10+73+6\frac{10+\sqrt{7}}{3+\sqrt{6}}3+610+7
- Simplify. 11+1310−4\frac{11+\sqrt{13}}{10-\sqrt{4}}10−411+13
- Simplify if a,b,c,d>0a,b,c,d>0a,b,c,d>0. a+bc+d\frac{\sqrt{a}+\sqrt{b}}{\sqrt{c}+\sqrt{d}}c+da+b
- Simplify. 1−221+5\frac{1-2\sqrt{2}}{1+\sqrt{5}}1+51−22
- Remove the radical from the denominator by multiplying by the conjugate: 11+2\frac{1}{1+\sqrt{2}}1+21
- Remove the radical from the denominator by multiplying by the conjugate: 43+5\frac{4}{3+\sqrt{5}}3+54
- Remove the radical from the denominator by multiplying by the conjugate: 33−1\frac{\sqrt{3}}{\sqrt{3}-1}3−13
- Remove the radical from the denominator by multiplying by the conjugate: 42−2\frac{4}{\sqrt{2}-2}2−24
- Remove the radical from the denominator by multiplying by the conjugate: x−yx+y\frac{x-y}{\sqrt{x}+\sqrt{y}}x+yx−y
- Remove the radical from the denominator by multiplying by the conjugate: 2+62+3\frac{2+\sqrt{6}}{2+\sqrt{3}}2+32+6
- Which two of the following are conjugates of the expression 4−34-\sqrt{3}4−3?
- Which two of the following are conjugates of the expression 2−3\sqrt{2}-\sqrt{3}2−3?
- Which two of the following are conjugates of the expression 2−π\sqrt{2}-\pi2−π?
- Concept check: When rationalizing a fraction with conjugates, you multiply the ‾\underline{\ \ \ \ \ \ \ \ } of the fraction by the conjugate.
- Rationalize the function y=x1−xy=\frac{\sqrt{x}}{1-\sqrt{x}}y=1−xx
- Rationalize the function y=8−2x2+xy=\frac{8-2x}{2+\sqrt{x}}y=2+x8−2x
- Two conjugates of the form a±ba \pm \sqrt{b}a±b have a sum of 444 and a product of 111. What are the conjugates?
- Two conjugates of the form a±ba \pm \sqrt{b}a±b have a sum of 101010 and a product of 151515. What are the conjugates?
- Rationalize the function y=x2+3y=\frac{x}{2+\sqrt{3}}y=2+3x
- One way to solve a quadratic equation is to use the quadratic formula: x=−b±b2−4ac2ax=\frac{-b \pm \sqrt{b^2-4ac}}{2a}x=2a−b±b2−4ac If x1x_1x1 and x2x_2x2 are the solutions …
- Solve equation (A) and plug the result into expression (B). x(2+3)=3(A)23−x(B)\begin{array}{lc} x(2+\sqrt3)=\sqrt3&\quad\small{(A)}\\ 2\sqrt3-x&\quad\small{(B)} \end{array}x(2+3…